Might Lee have been cut off on the wrong side of the Potomac and forced to surrender or have his army destroyed?
Quite easily. In fact, it's almost a miracle that this didn't happen IOTL. It took a combination of absurd vacillation on the part of McClellan and absurd luck on the part of Lee, to say nothing of unbelievable fighting on the part of Lee's soldiers, to allow the Army of Northern Virginia to get back to Virginia in one piece.
IF SO would JEF dAVIS have surrenedered.
Not right away, no. The war would continue into 1863. I would imagine that McClellan would get down to the Rappahannock/Rapidan River line before going into winter quarters. Richmond won't be besieged until the spring. The Confederates would scrap together an army to defend Richmond, but that means forces would have to be taken from elsewhere, which means that the South probably loses the whole of Tennessee and perhaps the Mississippi River before 1862 is over.
My guess is that the Confederacy collapses sometime around the summer or fall of 1863, barring anything truly surprising.
What would be the political impact?
President McClellan in 1864, on a platform to basically restore the status quo antebellum.